Typos (typing wrong when one knows better) are only one class of error in texts. Mental errors (mindos) are actually more likely to end up in a published book. My recent posts about errors in published books mostly discussed word-substitution errors, which I sometimes call "oops" words. "Oops" words can be typos or mindos. Another class of mindo is mistaken knowledge, where the author or editor thinks a particular word or fact is correct when it is wrong.
A 2003 category romance provides an example of a knowledge error that can be fixed by changing a single word. An early-evening scene is described with an almost-full moon in the western sky. Just change western to eastern and the astronomical glitch goes away.

I (and other people) have suggested before that publishing could benefit from a beta-testing system. If books had version numbers like a lot of software, I would say the finished manuscript (or file) from most authors is a 0.9 version and the manuscript after editing is a 1.0 version. (Some authors with good proofreading skills produce 1.0 level manuscripts, and some who need a lot of editing produce versions lower than 0.9.) It is almost impossible for a few people to spot all problems in a few readings of any large document. This is especially true for factual/historical errors, but can even apply to grammar. A small group of people (an author and one or a few editors) simply wonít have as much knowledge as the eventual pool of readers of a published book. Readers with specialized knowledge will spot science errors, title errors, geography errors, climate errors, botany errors, horsemanship errors, etc. If publishers provided an easy feedback mechanism their books could benefit from the knowledge of readers. Then the publishers could release version 1.1 (or 2.0 if there are a lot of changes) of the book. This should be relatively easy with ebooks. It even happens occasionally with print publishing. Samuel R. Delanyís Dhalgren and an early Eloisa James book come to mind (if Iím recalling correctly). I seem to recall reading years ago that multiple rounds of corrections to Dhalgren wiped out profits from the paperback printings, but that could be an urban legend.
I have been sending the errata I notice to the editor of the Grantville Gazette ever since I was given contact info a few years ago. I also got thanked for errata I sent to the authors of a free story on an author web site, so I know that there are actually authors and publishers who will correct texts after a release.
In print, I saw the opposite of perfectibility with the Harlequin Heyer reprints of the early 2000s. The books were very nice in many ways, replacing our falling-apart older copies with more readably sized text, but they introduced dozens of NEW errors. (I checked against our older copies from other publishers.) This is an example of source-specific degradation of text.
Production (manufacturing) errors include binding errors in printed books where a signature (block of pages) is missing or misplaced. In ebooks, I have seen missing and misplaced chapters and other large blocks of misplaced text. I have also seen smaller blocks of text missing. Missing text can only be fixed if a copy of the work containing the missing part exists somewhere or the author is available to ask. I got a couple Harlequin ebooks from Kobo that had major blocks of text missing. When I contacted Harlequin, they said they had provided corrected ebooks to all sellers, but Kobo didn't correct their available downloads when I contacted them, so this is a different example of source-specific degradation of text.

I know of at least one source of ebooks that already has a system in place for readers to submit errata: Project Gutenberg. They welcome corrections, and their FAQ page describes how to submit them.

Much as I might wish to see perfected texts, I can't help thinking about practical issues.
Many textual errors are unambiguous, but there are also some that can only be resolved by asking the author what was intended. Can living authors be expected to spend much time fixing older works instead of writing new works? What do you do when the author is no longer living? Who has the legal right to say what to do with the text? If a text is in the public domain, does anyone have a moral right to change the text to fix ambiguous errors?
What about errors that require some rewriting to fix? In Heyer's set of connected Georgian/Regency books, there is a timing problem between the earlier books and An Infamous Army. The h/h of Devil's Cub are described as the grandparents of Barbara in AIA, but there aren't enough years between the stories to squeeze in an intervening generation. Changing grandparents to parents would only require a few paragraphs to be rewritten, but should it be rewritten or should a perfected text just add a footnote about the known timing problem?
Unambiguous error fixes include spelling and punctuation to form correct English sentences and word substitutions where there is a clear and obvious correction. Even these can have gray areas.
Should quoted dialogue be corrected or left untouched? Should narration in a character's (as distinct from an author's) voice be corrected or left untouched? (E.g., Whispers Under Ground by Ben Aaronovitch has several me/I errors in first-person narration and one bit of text showing that the character is confused about the correct usage.)
How strictly should period language be enforced in fiction with historical settings? English has changed so much over time that for any setting more than a couple centuries from the present it is much easier to just use current English rather than try to accurately reproduce the language of the time. Where does one draw a line? How much period slang is appropriate? (Too many stories set in the English Regency have socially inappropriate use of slang and thieves' cant.) How much modern psychological jargon is acceptable? (For me, any psychobabble in dialogue set before the late 1800s is an anachronism.)
The use of "flawn" (a custard like flan or a pancake) in several Regency-set books is an interesting case. A dictionary check found "as flat as a flawn", but many books have "as fat as a flawn". I believe Heyer introduced this, but have no way of knowing if it was an error or her part or one of her deliberate traps for other authors copying from her. Should all these instances be treated as errors, or should the current frequency of the "fat" usage be treated as language evolution?
What about regional English? The largest subset of the fiction market is written in the United States for readers in the United States, but is it really appropriate to use American English in stories set in England, Canada, Australia, New Zealand, South Africa, India, Japan, or wherever? Equally, is it appropriate to use British English in books written outside the U.S. but set in the U.S.? I've noticed that some recent Harlequin Historical ebooks written by American authors are in British English. (See Wikipedia for examples of the differences. A few obvious ones are -ize vs. -ise, o vs. ou in several words, and vice vs. vise. I've also read that "gotten" is an Americanism.) Beyond the many versions of English around the world, should more effort be made to use regional English from different parts of the U.S.?
What about punctuation styles, such as single or double quotes? There are many "correct" or "standard" rules, but there are also many choices set in a publisher's or publication's style. Is there such a thing as a truly "standard" version that all authorities agree on for American English?

In response to the question in the subject line: I don't think a perfect text is even desireable let alone possible. A perfect text, IMO, would be one in which there were no errors whatsoever, including fragments, punctuation problems, switched words, mistaken homophones--anything at all. And that kind of text, it seems to me, would probably make for a very dull style.

For some authors--Laurens, for example--sentence fragments fragments are integral to her excited, breathless, sometimes nearly inchoate style. If made perfect, the text wouldn't be Laurens' at all.

Off the top of my head, the only writer I can think of who might be able to write a perfect text in an interesting style might be Samuel Johnson, whose prose flows in Latinate splendor.

I wear a badge for the grammar police daily, but I also admire idiosyncrasies of style greatly--when they work.

I don't know. Recognizing, though, that an author doesn't know the difference between objective and subjective cases usually makes me cringe for the state of the language. In an exchange on the net, I once pointed out to an author that what she called the passive voice wasn't and was roundly rebuked and told it didn't matter anyway. How dare I?

Recognizing, though, that an author doesn't know the difference between objective and subjective cases usually makes me cringe for the state of the language.

That's the foundation of the sentence, which is the first step in good dialogue. When those cases are understood, usually the rest can fall into place naturally (or not). I don't know anymore. There are times when I'm posting somewhere and use incomplete sentences. Not good (see, an incomplete--or is "it is" understood?).

How to treat dialogue and narrator's language are two of the areas that I included as questions. My own preference would be to leave most dialogue lightly edited. Keep sentence fragments, since people do speak that way. Fix word substitution errors unless they are clearly intended to convey aspects of a character like Spoonerisms or Malapropisms or the me/I example I gave.
I should have clarified that for me a text would be perfect if it conveyed exactly what the author wanted to convey, with no distracting spelling, grammar, punctuation, wrong word, historical, scientific, cultural, or continuity problems.

I suppose The Lord of the Rings is as close as it gets to a perfect text in terms of word usage and lack of errors (if you don't mind lots of old-fashioned phrases). But most books are not written by Oxford philologists over the course of of more than a decade.

Ironically, the first American paperback edition I bought is full of publisher's typos

Perfect text is possible...depending on how much time you have. Money's another issue. I think most kinds of print publishing are under deadline pressure...or...a mistake found at a later point in the process may be let go because of costliness. Oh, and delivery deadlines factor in too.

Many years ago we let a magazine go to press with too many known errors because of delays that had been caused back then by horrendous mainframe computer problems. It was either print it and ship it, or miss on-sale altogether (and it was a time oriented magazine). It only happened once but it was huge deal for the time.

On the other hand, language is a living thing that constantly changes, and how an individual uses it is all part of communication. I have wondered, though, about all the changes in the speed of communication these days and if people at some time will cease to care or care less about what's perfect or darn close.

Based on a couple of linguistics classes and a long time spent teaching English overseas with a variety of Native English speakers from all over the globe, as well as having written a couple of novels myself, I have to say that "perfect" text is a myth, just like "correct" English. The English we feel is "correct" is the English we were taught in school, but those rules are based on societal agreement that is ever changing. That old saw about never ending a sentence with a preposition was based on the notion that Latin is a perfect language and in Latin you cannot end a sentence with a preposition. English is not Latin and over time, that rule has been discarded. The Standard American English dialect uses lay and lie incorrectly. According to the current rule, it's still wrong, but how long will it be before that rule gets eliminated? Dreamt and leapt were accepted past tense versions of their root words (along with slept and kept), but they are falling out of favor and my computer always tries to correct me when I use them. (I shudder for the day when slept gets leveled into sleeped.) Alright and all right used to have distinctly different meanings, but for some reason "alright" is now not accepted and I am forced to change it regularly. And none of this gets into South African English, Australian English, New Zealand English, Scottish English, Standard British English and all the other dialects with their dropped letters, different word orders, local word meanings and missing phonemes.

If you want to read a perfect text, you'll have to read it in a dead language because English evolves constantly and at different rates in different directions in different places. That's what makes it so fascinating._________________Angsty romance with scattered humor.
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I agree with most of the posts- nothing will ever be perfect and as mentioned, how will we laugh at the mistakes if there are none?
I don't see however the point about correcting dialogue of a character or first person narrative. If that is how they speak, that is how they speak. If she says that she is going to "lay down" for a while - that is what all the people around her probably say. To correct her dialogue to say "I am going to lie down" would be incorrect for that character in the story. However, if the author writes that "Mary decided to lay down for a while." then we should feel free to correct the author.

Yes, English does evolve. Latin didn't and it is a dead langauge. I used to teach Spanish - a language that has a "Real Academia" that decides what is and isn't correct Spanish. This very august group of known writers and grammatists endeavors to control what is and isn't accepted as standard Spanish. After about 100 years, sometimes they let in new words and spellings (a little exagerrated). eg. they do not accept "computadora" that is used in Latin America. In Spain it is "ordinadora" A similar word exists in French as well. Also, English can take a verb and start to use it as a noun and it is accepted, and vice versa - speakers of correct Spanish do not accept that- hence you can have an "apertura" (opening) but not "aperturar." (used as in to open something or to inaugerate).
I once read that a language must open the flood gates once in a while and let in new blood to keep alive.

Yes, languages are living, changing things, as Latin once was. But in my view, perfect text occurs when the author can clearly convey what she means to say without any typos, wrong word choices (because of exact meaning or "color" of the word) or any grammatical illiteracies for the time in which it is written. Some language usages are in flux, of course, but generally there are acceptable variations over periods of time.

If you want to read a perfect text, you'll have to read it in a dead language because English evolves constantly and at different rates in different directions in different places. That's what makes it so fascinating.

I've been lurking in this thread but have to give a nod of agreement here, well said.

Linda_________________"The Bookshop has a thousand books, all colors, hues and tinges, and every cover is a door that turns on magic hinges." ~ Nancy Byrd Turner

Yes, language grows and changes, and sometimes those changes are godawful. But, surely clarity in communicating is the most important factor to consider, and clarity in communicating is best achieved by following the "rules." Yes, we can end sentences with prepositions and the meaning isn't changed much, but logic of relationships is. For example, /that is the house which he resides in/ doesn't change the meaning much, but /that is the house in which he resides/ preserves the logic of the relationships better.

I agree that it's very unlikely that a perfect text could be created; I don't even know whether one is desirable. But I also think language is a gift of such inestimable value that we should touch it only with kindness and resist its sliding into barbarisms wherever they are encountered.

Yes, I agree clarity is the word. And I also agree that while perfection in language (or anything) may be hard or perhaps impossible to achieve, I don't think we should ever stop trying for it. It can be so beautiful and too precious not to. And we have some previous writers of such beautiful prose and poetry to try to emulate. Why not go for it?